1. Field of the Invention
The present invention relates to a method for evaluating a pattern dimension, a method for evaluating roughness of a pattern edge, or a method for evaluating fluctuation of a local size of a pattern, by performing a nondestructive observation and an image processing using a scanning microscope and an atomic force microscope and an apparatus for data analysis that can realize these methods.
2. Description of the Related Art
In the semiconductor industry and other industries, a need to accurately define a pattern shape (hereinafter, referred to as a pattern shape index) has been raised with the fineness of a pattern processing dimension. As the index indicating the pattern shape (hereinafter, referred to as a pattern shape index), there may be a degree of fine roughness of a pattern edge that is randomly generated, the roughness being referred to as edge roughness, a local dimension caused due to the above-mentioned roughness, sharpness of a roughness shape, etc., in addition to the pattern dimension.
However, the above-mentioned degrees are particularly important to a gate of a transistor or an interconnect pattern that requires fineness. The deviations from a design shape of the pattern shape occur in the gate pattern of the transistor, such that the performance of the transistor is deteriorated or distributed. Further, the deviations in the interconnect pattern reduce the lifespan of the devices.
In most cases, since these patterns are line patterns, the above-mentioned pattern shape index may be considered to be the finest line pattern dimension (in general, critical dimension called CD) that is created in a manufacturing process, a degree of line-edge roughness (LER), a degree of line-width roughness (LWR), or a spatial frequency of LER, LWR, hall edge roughness, etc. The definition of the pattern shape index (calculation sequence) will be described in detail below. Even if these amounts can also be defined on the hall pattern, it is assumed to be the line pattern for clarity.
First, a process that takes out a pattern edge with a two-dimensional shape from a pattern with a three-dimensional shape will be described. These indices are obtained as follows. As shown in FIG. 1, a plane on which a base of a pattern is provided is assumed to be an xy plane. Further, a direction along a line is assumed to be a y direction, a vertical direction is assumed to be an x direction, and a direction vertical to the xy plane is assumed to be a z direction. If the pattern is cut on the plane that is z=H, as shown in FIG. 2, an area 204 becomes a field of view. Each of the line edges 201 and 202 is a left edge and a right edge. Various kinds of indices indicating characteristics of the pattern shape are obtained from a curve indicating the position of the edge points.
Although a true pattern edge is a set of continuous points as shown in FIG. 2, in order to practically evaluate the shape, these should be transformed into discrete data. The process will be described. First, an inspection area is determined. The pattern edge is determined within the range. Since the inspection area may be equal to a field of view, it is assumed that the inspection area herein is equal to the field of view.
The pattern edges existing in the inspection area are represented by n points. In other words, a sampling interval is defined as Δy and a straight line is represented by the following Equation 1.y=i·Δy (i=1, 2, . . . n)  [Equation 1]
This straight line assumes that a point intersecting with a line edge 201 or 202 is an edge point xLi or xRi. Subscripts L and R represent a left edge and a right edge, respectively. Various kinds of indices indicating the characteristics of the patterns can be defined from a set of these discrete points. When LER(3σ), spectrum, etc., are obtained, there is a need to calculate an approximation straight line of 201 or 202. To this end, a straight line best describing this is obtained using a set of points {(xji, iΔy)|i=1, 2, . . . n} (j=R or L). A well known method is a least square method. Next, a difference between the edge point xLi or the edge point xRi and an x coordinate of an approximation straight line is calculated on each straight line represented by Equation 1. The difference (hereinafter, it is marked by a deviation amount of the position of the edge points) of the x coordinate obtained from the line edge 201 is assumed to be ΔxLi and the deviation amount of the position of the edge points obtained from the line edge 202 is assumed to be ΔxRi (i=1, 2, . . . n). The degree of LER is mainly represented as three times as large as a standard deviation of a distribution of ΔxLi or ΔxRi. Further, the degree of LWR is mainly represented as three times as large as a standard deviation of a distribution of a local line width wi represented as follows.wi=xRi−xLi  [Equation 2]
Hereinafter, these indices are described as the LER(3σ) and the LWR(3σ). Further, as amounts indicating the characteristics of the LER (or LWR) shape, there are skewness (hereinafter, represented by γ) of the LER (or LWR) distribution, a correlation length (hereinafter, represented by ξ) of the LER (or LWR), etc. γ is skewness (third order moment) of a histogram of ΔxLi, ΔxRi or, wi. Further, ξ is provided by the following Equation 3 for p values that are determined by a user.p=∫Δx(y)Δx(y−ξ)dy  [Equation 3]
As the p values, values such as 1/e, 0.2, 0 are mainly used. Further, in the above Equation 3, ΔxRi or ΔxLi is represented by Δx. y has a relationship with i as in Equation 1. In the actual calculation, it is obtained as a sum of discrete amounts rather than an integration of a continuous function.
Moreover, the height of the pattern is constantly approximated in any cross sections and one that divides H by the height of the pattern (for example, a maximum value of actually measured values, etc.) is represented by h. Hereinafter; values representing a distance from a substrate of a plane are represented by h, which will be described below.
Further, the method for determining the above-mentioned edge is ideal, but a method or a sequence that transforms a true three-dimensional shape into a two-dimensional shape (edge), a set of continuous points into a set of discrete points may be any of various methods or sequences. In addition, the noise reduction of the image is performed by performing various kinds of image processes on data before extracting the position of the edges.
In general, the above-mentioned indices can be evaluated using a scanning electron microscope having a length measuring function. This tool is called a critical dimension scanning electron microscope (CD-SEM). However, an image obtained through observation with the CD-SEM is a sky observation image. To be exact, ξ or γ of CD, LER(3σ), LWR(3σ), LER or LWR is a function of h, but it is difficult to obtain the index values when h is directly specified from the CD-SEM observation image. However, even when it is assumed that the pattern is considered to be the ideal line and the pattern shape is hardly changed in a height (z) direction, there is no problem.
When the pattern dimension becomes small, the three-dimensional structure of the created pattern has a great effect on the performance of the device. Therefore, when the position along the height direction of the pattern, that is, h is specified in the semiconductor inspection, there is a need to obtain the foregoing index values. Hereinafter, these amounts are represented by the functions of CD(h), 3σ(h), ξ(h), γ(h), and h.
As described above, in a semiconductor mass-production process, the CD-SEM has been used as a tool for inspection and metrology. Meanwhile, as a tool for measuring a fine structure, an atomic force microscope (AFM) has been known well. Further, as the tool for measuring a fine structure, in addition to the AFM, a scanning probe microscope (SPM) such as a scanning tunneling microscope (STM) has been known. However, in the present specification, the AFM will be described as one example of the SPM.
The advantages and disadvantages of each of the CD-SEM and AFM will be described below.
First, the CD-SEM has a high throughput. Further, it has an incident beam diameter smaller than 2 nm. In other words, it has very high resolution. A measurable line length (maximum value) is several microns, which is also sufficient to measure CD values, LER(3σ), or LWR(3σ). Meanwhile, there is a disadvantage in that it is impossible to directly measure the three-dimensional shape. Essentially, if a set of points (x, y, and z), which form the pattern surface within the three-dimensional space is provided, it is in principle possible to create the CD-SEM images by estimating and simulating electron beams incident thereon. However, the simulation itself is very difficult and inverse transform is much more difficult. In other words, the three-dimensional information is included in the CD-SEM images, but it is difficult to take out the three-dimensional information.
On the other hand, the AFM can directly measure the three-dimensional shape. The resolution depends on a radius of curvature of a tip of a probe used, but recently the probe has been created to have a size of 2 nm. In other words, there is sufficient resolution. However, the throughput decreases and there is drift of the signal, such that the line length can only be accurately measured to about 200 nm. Further, the line length that can be measured is a trade-off in respects to accuracy.
As described above, the AFM has suitably been used recently to evaluate the required three-dimensional shape. As described above, it is difficult to directly transform the three-dimensional shape data such as in the AFM by transforming the CD-SEM images. However, for the inspection in the semiconductor mass-production process that is necessary to observe the long line and requires high throughput, there are no solutions other than the method of using the CD-SEM.
An evaluation and optimization method for these measurement tools such as CD-SEM and AFM is disclosed in JP-T-2006-510912 and a comparative example of the LERs of the CD-SEM and the AFM is described in “C. Nelson, et al., Journal of Vacuum Science Technology, B17, pp. 2488-2498 (1999)”.